One challenge of legged locomotion on uneven terrains is to deal with both the discrete problem of selecting a contact surface for each footstep and the continuous problem of placing each footstep on the selected surface. Consequently, footstep planning can be addressed with a Mixed Integer Program (MIP), an elegant but computationally demanding method, which can make it unsuitable for online planning. We reformulate the MIP into a cardinality problem, then approximate it as a computationally efficient ell 1-norm minimisation, called SL1M. Moreover, we improve the performance and convergence of SL1M by combining it with a sampling-based root trajectory planner to prune irrelevant surface candidates. Our tests on the humanoid Talos in four representative scenarios show that SL1M always converges faster than MIP. For scenarios when the combinatorial complexity is small (< 10 surfaces per step), SL1M converges at least two times faster than MIP with no need for pruning. In more complex cases, SL1M converges up to 100 times faster than MIP with the help of pruning. Moreover, pruning can also improve the MIP computation time. The versatility of the framework is shown with additional tests on the quadruped robot ANYmal.
Bibliographical noteFunding Information:
Manuscript received November 16, 2020; accepted May 2, 2021. Date of publication June 14, 2021; date of current version June 23, 2021. This letter was recommended for publication by Associate Editor T. Bandyopadhyay and Editor N. Amato upon evaluation of the reviewers’ comments. The work of Daeun Song and Young J. Kim was supported in part by the ITRC/IITP program (IITP-2021-0-01460) and the NRF (2017R1A2B3012701) in South Korea. The work of Pierre Fernbach, Thomas Flayols, Andrea Del Prete, Nicolas Mansard and Steve Tonneau was supported by the H2020 project Memmo (ICT-780l684). (Corresponding author: Young J. Kim.) Daeun Song and Young J. Kim are with the Department of Computer Science and Engineering, Ewha Womans University, Seoul 03760, South Korea (e-mail: email@example.com; firstname.lastname@example.org).
© 2016 IEEE.
- Humanoid and bipedal locomotion
- legged robots
- motion and path planning